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Steve Ritter '85

I think if you ask most high school students what mathematicians do, they'd say "solve really hard equations." Despite being a pretty good math student in high school and having some extra-curricular interests in fields like topology, I probably would have given the same answer when I was in high school. Like many students, I didn't realize that the things I found most interesting about math were also the things that mathematicians did. The skills-based academic curricula provide the means to do interesting work in mathematics, but skills aren't what the field is about.

Tom Banchoff was largely responsible for helping me realize that the mathematical concepts that I found interesting were also worthy of being taken seriously. This was the essence of his Mathematical Way of Thinking course and also his contribution when, as part of a computer graphics course, Kevin Pickhardt and I developed a program to graph three- and four-dimensional surfaces, given an implicit equation. Kevin and I implemented the program, but Tom provided the fundamental insight that made the algorithm work. He taught us to treat the surface as a real object situated in space. This was a simple, but crucial, change in perspective for us.

Kevin and I had tested the system on spheres and the occasional torus, but Tom wanted to put the software to work right away. He immediately entered the equation for a surface mentioned (but not illustrated) in a paper he was reading (well, it wasnÕt quite immediate — we first needed to expand the size of the text field to accommodate the equation). The three of us anxiously stared at the screen as the surface started to render. Panic initially set in when Tom muttered, "wait, thatÕs not it," but as the full image appeared and was rotated to a better viewing angle, we were satisfied and relieved that the program worked.

I was a Cognitive Science major at Brown and earned a Ph.D. in Cognitive Psychology at Carnegie Mellon University in 1992. In retrospect, perhaps it is not surprising that I was able to combine my interest in cognition with my interests in math. As a post-doc, I started developing cognitive models of how students thought about mathematics and incorporated them into "intelligent tutoring systems" that help students learn math. These systems became successful enough to lead to a business (Carnegie Learning, where I now work). Our "Cognitive Tutors" are now being used as primary curricula in over 1500 schools.

The focus, of course, is on mathematical concepts. In an indirect way, I think these courses are helping to transmit the kind of excitement and vitality that Tom Banchoff helped me see in mathematics to a new generation of students.

— Steve Ritter
October 2003

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Created: 11 Oct 2003
Last modified: 25 Oct 2003 15:39:02
Comments to: dpvc@union.edu
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